Joint distribution of multiple random variables

Wogie

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Joined
Sep 8, 2018
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Hi. I'm asked to find the joint distribution pX,Y,Z of the independant random variables:
pX = Nx
pY = -X + Ny
pZ = X + 2Y + Nz

Where Nx, Ny, Nz are independant noise terms from the normal distribution N(0,1)

My initial guess is to use conditional probability p(A|B) = pA,B / pB. This gives me

-X+N_Y = pX,Y / Nx
=> pX,Y = (-X+N_Y)N_X

and

X+2Y+N_Z = pZ,(X,Y) / ((-X+Ny)Nx)
=> P(Z,(X,Y)) = (X+2Y+Nz)(-X+Ny)Nx

But I have no idea if this is correct. How would you approach this?

/ Lasse
 
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